Electric Motor Comparison: Theory
Introduction
The performance of electric motors can be characterized by several measures: efficiency, maximum output power and torque, speed regulation and power factor. Measurement of efficiency requires measurement of the power input to and output from the motor. Input power is easily determined for electric motors from the supplied voltage and current. Output power and torque are usually measured by dynamometers, which are also the most widely used devices for power and torque measurements on internal-combustion engines, steam turbines, etc. Speed regulation is a measure of how constant the speed of the motor is when subjected to increased loads. Power factor refers to the phase relationship of voltage and current drawn by the motor. If too low, the power factor can result in additional electric utility charges.
Note: Remember to report the uncertainty of all measurements and calculations.
Theory and Analysis
The experimental setup consists of two interchangeable AC-motors (1/2 and 3/4 horsepower) whose performance is measured by a one horsepower dynamometer/generator. The dynamometer, or “dyno” as it is called in the automotive industry, is basically a DC generator coupled to a force-measuring device, such as a weight scale or load cell that is used to measure the torque produced by the AC-motor. The electrical output of the dynamometer/generator is connected to power-dissipating resistors that create a load that the AC-motor must overcome. DC generators operate by applying moving a conductor through a magnetic field. In a dynamometer, the magnetic field can be varied, resulting in a variable load. By adjusting the so-called excitation current, one can apply a varying load to the AC-motor being tested.
The torque is measured by measuring the force exerted through a moment arm attached to the outer casing of the dynamometer. In our case both a mechanical scale and load cell are available to measure the force. The power generated by the AC-motor is obtained from the dynamometer according to the following equation:
(1)
where,
Pg - output power, hp,
R - lever arm (0.500 ft.),
L - indicated load, lbf,
N - rotational speed, rev/min.
The 33,000 is a unit conversion factor that ensures that the power is in units of horsepower (what would the conversion factor be if the desired units were watts?).
The tachometer of the dynamometer shaft has an optical transistor that switches between 0V and 5V depending on whether one of the 20 teeth of the rotating gear is blocking the path of the light sensor. The tachometer measures the number of 0-5V pulses within a given amount of time to determine the speed of the rotating shaft. An important motor characteristic is speed regulation, which is defined as how well the motor maintains its speed when subjected to different loads.
1) Calculate the average speed for each load condition and estimate the speed uncertainty.
2) Compute the speed of each motor at each load condition as a percentage of the rated speed of the motor. The rated speeds and rated powers are listed on the metal name plate of the motor.
3) On the same graph, plot the percent of rated speed versus output power (in hp) for all load conditions for each motor. Similarly, plot the percent of rated speed versus percent of rated power for both motors for all loads on the same plot. Analyze and discuss these two plots.
The maximum possible power that can be delivered to the motor is known as the apparent power. The actual power consumed by the motor is referred to as the average power (discussed later). The apparent power delivered to the motor may be calculated using the root-mean-square values of the current and voltage supplied to the motor as shown in the equation below:
(2)
where Papparent is in watts, Irms is in amps, and Vrms is in volts.
4) Calculate the apparent power (in hp) for each motor for all output power settings (in hp).
The average power consumed by the motor can be found by taking the dot product between the current and voltage, Equation 3. Average power can also be found by averaging the instantaneous power consumed by the motor. The instantaneous power of the motor is simply the instantaneous voltage multiplied by the instantaneous current, v(t)×i(t).
If the current and voltage are in phase, the average power equals the apparent power. If the voltage and current delivered to the motor are not in phase, the disparity between the average power and the apparent power provides a measure of the power factor, Equation 4. The power factor is related to the phase angle, q, between the sinusoidal waveforms of the current and the voltage and is defined as the ratio of the average power to the apparent power.
(3)
(4)
I = the current in amps,
V = the voltage in volts,
q = phase angle between current and voltage
The angle q in Equations 3 and 4 is known as the power factor angle and is the phase angle of the load impedance. The phase angle, q, can vary between +90° and -90°; therefore, the power factor can vary between 0 and 1 [4].
Estimating uncertainty in average power must be done differently than previous uncertainty calculations because average power is a sine wave. One way to estimate the uncertainty is to (1) calculate the average power for 10-15 individual cycles, and then (2) calculate the standard deviation in these 10-15 Pave values.
5) Calculate the average power (in hp) delivered to the motors for all output power settings (in hp).
6) Calculate the power factor for the motors at the different output power settings. Construct a plot of the power factor versus output power (in hp). Discuss the relationship.
The efficiency of the motor is defined as
(5)
7) Calculate the efficiency of each motor for all output power levels. Plot the efficiency versus the output power for both motors in a single figure. Discuss the characteristics of the curves and what variable was used as the “input power.”
Remember that these questions are designed to help you in preparing your report. Your report should not be merely a restatement of the questions with the answers.
References
1. J.P. Holman, Experimental Methods for Engineers, 5th Ed., McGraw-Hill, New York, 1989, p. 397.
2. T.R. Beckwith and R.D. Marangoni, Mechanical Measurements, 4th Ed., Addison-Wesley, Reading, MA, 1990, p. 489.
3. E.O. Doeblin, Measurement Systems, Application and Design, 4th Ed., McGraw-Hill, New York, 1990, p. 425.
4. J.D. Irwin and D.V. Kerns, Jr., Introduction to Electrical Engineering, Prentice Hall, Englewood Cliffs, New Jersey, 1995, pp.179-180.
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